Phase locking of nonlinear monopoles with reactive coupling

Abstract

Recently it was shown that a system of coupled nonlinear acoustic oscillators such as bubbles in a liquid may generate a coherent radiation starting from the initially incoherent state. However, such an active (radiative) coupling is typically weak, especially if the size of the system is smaller than the acoustic wavelength. Here a stronger, reactive coupling, such as an interaction of bubbles via the potential fluid motion around them, is considered. It is shown that an initial incoherent phase distribution is unstable only for the excitation level exceeding a definite threshold. For a nonlinear stage of generation a three-mode analytical model is used, permitting one to perform a phase-plane investigation of a system and to estimate the amplitude and duration of the generated coherent pulse. From the viewpoint of nonlinear dynamics, such an effect is an example of a ‘‘chaos–order’’ transition in a Hamiltonian system (although chaos may be just a lack of coherence). The role of small dissipation is also considered. Some estimates are made for the ensemble of bubbles in a liquid. a)Now at Univ. of Colorado at Boulder, CIRES, ETL/ERL/NOAA, 325 Broadway, R/E/ET, Boulder, CO 80303.